PAPER BY PROF. OBERBECK. 155 



as the analytical expression for this quantity, omitting a factor that 

 depends upon the adopted units, and in which dn is an element of the 

 normal to the curve whose equation is i? / p=constant. 



I put 



r = ^^'':=L/(^^Y+(«Y 



p dn py\JxJ^\J!/J 



Furthermore, let the velocity of the wind at a point d? y be <i? so that 

 <i;2=;(2-|-r- and let e be the angle between go and ;/, in which y must 

 indicate the direction of diminishing pressure. Then we have 





n^P + v 



or 



cos 6= . . . /a\ 



^ P\ J'l' ?yj 



If we multiply the first of equation (.l) by xi and the second by v and 

 add together, there results, 





or 



7 , ?IGO ?)00 /)(i9 



y cos e = /va7+^_|_M — + vV- 

 for which by introducing the notation 



we can write 



(It dt dx ^y 



1 , d(sD ,ov 



y COS e = kQj-{-—^' (8) 



From these equations many consequences can be drawn that lead to 

 specially simple theorems when the velocities of the wind are so small 

 that the term 



«— + !', 



?x ;)y 



•can be neglected. But the following theorems will also be approxi- 

 mately true even if the velocities are larger, 



(a) If we compare an invariable system of wind and one that is va- 

 riable as to its intensity, and of \^hich we will assume that at any given 

 instant there prevails throughout it everywhere uniform velocities and 



L 



